%I #8 Dec 24 2015 10:13:22

%S 1,3,280,2627625,5194672859376,1903991899429620,

%T 1461034854396267778567973305958400,

%U 450538787986875167583433232345723106006796340625,146413934927214422927834111686633731590253260933067148964500000000,3752368324673960479843764075706478869144868251518618794695144146928706880

%N a(n) = (m(n)*n)! / (n!)^(m(n)+1), where m(n) is the largest prime power <= n.

%C Morris and Fritze (2015) prove that a(n) is an integer.

%H Howard Carry Morris and Daniel Fritze, <a href="http://dx.doi.org/10.4169/math.mag.88.4.285">Problem 1948</a>, Math. Mag., 88 (2015), 288-289.

%F a(n) = A057599(n) for n a prime power.

%e The largest prime power <= 6 is m(6) = 5, so a(6) = (5*6)! / (6!)^(5+1) = 30! / (6!)^6 = 1903991899429620.

%Y Cf. A057599.

%K nonn

%O 1,2

%A _Jonathan Sondow_, Dec 19 2015